Graphics.Rasterific.Shading:$sradialGradientWithFocusShader from Rasterific-0.6.1, B

Percentage Accurate: 89.9% → 95.4%

Time: 6.7s

Alternatives: 8

Speedup: 0.8×

• 49.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right) \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (- (* x x) (* (* y 4.0) (- (* z z) t))))

C

double code(double x, double y, double z, double t) {
	return (x * x) - ((y * 4.0) * ((z * z) - t));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (x * x) - ((y * 4.0d0) * ((z * z) - t))
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x * x) - ((y * 4.0) * ((z * z) - t));
}

Python

def code(x, y, z, t):
	return (x * x) - ((y * 4.0) * ((z * z) - t))

Julia

function code(x, y, z, t)
	return Float64(Float64(x * x) - Float64(Float64(y * 4.0) * Float64(Float64(z * z) - t)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x * x) - ((y * 4.0) * ((z * z) - t));
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x * x), $MachinePrecision] - N[(N[(y * 4.0), $MachinePrecision] * N[(N[(z * z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 89.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right) \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (- (* x x) (* (* y 4.0) (- (* z z) t))))

C

double code(double x, double y, double z, double t) {
	return (x * x) - ((y * 4.0) * ((z * z) - t));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (x * x) - ((y * 4.0d0) * ((z * z) - t))
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x * x) - ((y * 4.0) * ((z * z) - t));
}

Python

def code(x, y, z, t):
	return (x * x) - ((y * 4.0) * ((z * z) - t))

Julia

function code(x, y, z, t)
	return Float64(Float64(x * x) - Float64(Float64(y * 4.0) * Float64(Float64(z * z) - t)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x * x) - ((y * 4.0) * ((z * z) - t));
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x * x), $MachinePrecision] - N[(N[(y * 4.0), $MachinePrecision] * N[(N[(z * z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 95.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot z \leq 2 \cdot 10^{+302}:\\ \;\;\;\;\mathsf{fma}\left(x, x, \left(z \cdot z - t\right) \cdot \left(y \cdot -4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(z \cdot \left(z \cdot y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z z) 2e+302)
   (fma x x (* (- (* z z) t) (* y -4.0)))
   (* -4.0 (* z (* z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * z) <= 2e+302) {
		tmp = fma(x, x, (((z * z) - t) * (y * -4.0)));
	} else {
		tmp = -4.0 * (z * (z * y));
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * z) <= 2e+302)
		tmp = fma(x, x, Float64(Float64(Float64(z * z) - t) * Float64(y * -4.0)));
	else
		tmp = Float64(-4.0 * Float64(z * Float64(z * y)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z * z), $MachinePrecision], 2e+302], N[(x * x + N[(N[(N[(z * z), $MachinePrecision] - t), $MachinePrecision] * N[(y * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(z * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z z) < 2.0000000000000002e302

   1. Initial program 96.1%

      \[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right) \]
   2. Step-by-step derivation

      1. fma-neg 98.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, x, -\left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\right)} \]

      2. *-commutative 98.3%

         \[\leadsto \mathsf{fma}\left(x, x, -\color{blue}{\left(z \cdot z - t\right) \cdot \left(y \cdot 4\right)}\right) \]

      3. distribute-rgt-neg-in 98.3%

         \[\leadsto \mathsf{fma}\left(x, x, \color{blue}{\left(z \cdot z - t\right) \cdot \left(-y \cdot 4\right)}\right) \]

      4. distribute-rgt-neg-in 98.3%

         \[\leadsto \mathsf{fma}\left(x, x, \left(z \cdot z - t\right) \cdot \color{blue}{\left(y \cdot \left(-4\right)\right)}\right) \]

      5. metadata-eval 98.3%

         \[\leadsto \mathsf{fma}\left(x, x, \left(z \cdot z - t\right) \cdot \left(y \cdot \color{blue}{-4}\right)\right) \]

   3. Simplified 98.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, x, \left(z \cdot z - t\right) \cdot \left(y \cdot -4\right)\right)} \]

   if 2.0000000000000002e302 < (*.f64 z z)

   1. Initial program 58.3%

      \[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right) \]

   2. Taylor expanded in z around inf 70.5%

      \[\leadsto \color{blue}{-4 \cdot \left(y \cdot {z}^{2}\right)} \]
   3. Step-by-step derivation

      1. unpow2 70.5%

         \[\leadsto -4 \cdot \left(y \cdot \color{blue}{\left(z \cdot z\right)}\right) \]

      2. *-commutative 70.5%

         \[\leadsto -4 \cdot \color{blue}{\left(\left(z \cdot z\right) \cdot y\right)} \]

      3. associate-*l* 91.8%

         \[\leadsto -4 \cdot \color{blue}{\left(z \cdot \left(z \cdot y\right)\right)} \]

   4. Simplified 91.8%

      \[\leadsto \color{blue}{-4 \cdot \left(z \cdot \left(z \cdot y\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 96.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot z \leq 2 \cdot 10^{+302}:\\ \;\;\;\;\mathsf{fma}\left(x, x, \left(z \cdot z - t\right) \cdot \left(y \cdot -4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(z \cdot \left(z \cdot y\right)\right)\\ \end{array} \]

Alternative 2: 83.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z \cdot z - t\right) \cdot \left(y \cdot -4\right)\\ t_2 := x \cdot x - t \cdot \left(y \cdot -4\right)\\ \mathbf{if}\;z \cdot z \leq 10^{-76}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \cdot z \leq 2000000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \cdot z \leq 5 \cdot 10^{+113}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \cdot z \leq 2 \cdot 10^{+154}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \cdot z \leq 4 \cdot 10^{+233}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(z \cdot \left(z \cdot y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- (* z z) t) (* y -4.0))) (t_2 (- (* x x) (* t (* y -4.0)))))
   (if (<= (* z z) 1e-76)
     t_2
     (if (<= (* z z) 2000000000000.0)
       t_1
       (if (<= (* z z) 5e+113)
         t_2
         (if (<= (* z z) 2e+154)
           t_1
           (if (<= (* z z) 4e+233) t_2 (* -4.0 (* z (* z y))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((z * z) - t) * (y * -4.0);
	double t_2 = (x * x) - (t * (y * -4.0));
	double tmp;
	if ((z * z) <= 1e-76) {
		tmp = t_2;
	} else if ((z * z) <= 2000000000000.0) {
		tmp = t_1;
	} else if ((z * z) <= 5e+113) {
		tmp = t_2;
	} else if ((z * z) <= 2e+154) {
		tmp = t_1;
	} else if ((z * z) <= 4e+233) {
		tmp = t_2;
	} else {
		tmp = -4.0 * (z * (z * y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((z * z) - t) * (y * (-4.0d0))
    t_2 = (x * x) - (t * (y * (-4.0d0)))
    if ((z * z) <= 1d-76) then
        tmp = t_2
    else if ((z * z) <= 2000000000000.0d0) then
        tmp = t_1
    else if ((z * z) <= 5d+113) then
        tmp = t_2
    else if ((z * z) <= 2d+154) then
        tmp = t_1
    else if ((z * z) <= 4d+233) then
        tmp = t_2
    else
        tmp = (-4.0d0) * (z * (z * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = ((z * z) - t) * (y * -4.0);
	double t_2 = (x * x) - (t * (y * -4.0));
	double tmp;
	if ((z * z) <= 1e-76) {
		tmp = t_2;
	} else if ((z * z) <= 2000000000000.0) {
		tmp = t_1;
	} else if ((z * z) <= 5e+113) {
		tmp = t_2;
	} else if ((z * z) <= 2e+154) {
		tmp = t_1;
	} else if ((z * z) <= 4e+233) {
		tmp = t_2;
	} else {
		tmp = -4.0 * (z * (z * y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = ((z * z) - t) * (y * -4.0)
	t_2 = (x * x) - (t * (y * -4.0))
	tmp = 0
	if (z * z) <= 1e-76:
		tmp = t_2
	elif (z * z) <= 2000000000000.0:
		tmp = t_1
	elif (z * z) <= 5e+113:
		tmp = t_2
	elif (z * z) <= 2e+154:
		tmp = t_1
	elif (z * z) <= 4e+233:
		tmp = t_2
	else:
		tmp = -4.0 * (z * (z * y))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(z * z) - t) * Float64(y * -4.0))
	t_2 = Float64(Float64(x * x) - Float64(t * Float64(y * -4.0)))
	tmp = 0.0
	if (Float64(z * z) <= 1e-76)
		tmp = t_2;
	elseif (Float64(z * z) <= 2000000000000.0)
		tmp = t_1;
	elseif (Float64(z * z) <= 5e+113)
		tmp = t_2;
	elseif (Float64(z * z) <= 2e+154)
		tmp = t_1;
	elseif (Float64(z * z) <= 4e+233)
		tmp = t_2;
	else
		tmp = Float64(-4.0 * Float64(z * Float64(z * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = ((z * z) - t) * (y * -4.0);
	t_2 = (x * x) - (t * (y * -4.0));
	tmp = 0.0;
	if ((z * z) <= 1e-76)
		tmp = t_2;
	elseif ((z * z) <= 2000000000000.0)
		tmp = t_1;
	elseif ((z * z) <= 5e+113)
		tmp = t_2;
	elseif ((z * z) <= 2e+154)
		tmp = t_1;
	elseif ((z * z) <= 4e+233)
		tmp = t_2;
	else
		tmp = -4.0 * (z * (z * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(z * z), $MachinePrecision] - t), $MachinePrecision] * N[(y * -4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * x), $MachinePrecision] - N[(t * N[(y * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z * z), $MachinePrecision], 1e-76], t$95$2, If[LessEqual[N[(z * z), $MachinePrecision], 2000000000000.0], t$95$1, If[LessEqual[N[(z * z), $MachinePrecision], 5e+113], t$95$2, If[LessEqual[N[(z * z), $MachinePrecision], 2e+154], t$95$1, If[LessEqual[N[(z * z), $MachinePrecision], 4e+233], t$95$2, N[(-4.0 * N[(z * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z z) < 9.99999999999999927e-77 or 2e12 < (*.f64 z z) < 5e113 or 2.00000000000000007e154 < (*.f64 z z) < 3.99999999999999989e233

   1. Initial program 95.7%

      \[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right) \]

   2. Taylor expanded in z around 0 93.1%

      \[\leadsto x \cdot x - \color{blue}{-4 \cdot \left(y \cdot t\right)} \]
   3. Step-by-step derivation

      1. associate-*r* 93.1%

         \[\leadsto x \cdot x - \color{blue}{\left(-4 \cdot y\right) \cdot t} \]

   4. Simplified 93.1%

      \[\leadsto x \cdot x - \color{blue}{\left(-4 \cdot y\right) \cdot t} \]

   if 9.99999999999999927e-77 < (*.f64 z z) < 2e12 or 5e113 < (*.f64 z z) < 2.00000000000000007e154

   1. Initial program 96.9%

      \[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right) \]

   2. Taylor expanded in x around 0 79.0%

      \[\leadsto \color{blue}{-4 \cdot \left(\left({z}^{2} - t\right) \cdot y\right)} \]
   3. Step-by-step derivation

      1. *-commutative 79.0%

         \[\leadsto \color{blue}{\left(\left({z}^{2} - t\right) \cdot y\right) \cdot -4} \]

      2. *-commutative 79.0%

         \[\leadsto \color{blue}{\left(y \cdot \left({z}^{2} - t\right)\right)} \cdot -4 \]

      3. unpow2 79.0%

         \[\leadsto \left(y \cdot \left(\color{blue}{z \cdot z} - t\right)\right) \cdot -4 \]

      4. *-commutative 79.0%

         \[\leadsto \color{blue}{\left(\left(z \cdot z - t\right) \cdot y\right)} \cdot -4 \]

      5. associate-*l* 79.0%

         \[\leadsto \color{blue}{\left(z \cdot z - t\right) \cdot \left(y \cdot -4\right)} \]

   4. Simplified 79.0%

      \[\leadsto \color{blue}{\left(z \cdot z - t\right) \cdot \left(y \cdot -4\right)} \]

   if 3.99999999999999989e233 < (*.f64 z z)

   1. Initial program 63.3%

      \[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right) \]

   2. Taylor expanded in z around inf 72.9%

      \[\leadsto \color{blue}{-4 \cdot \left(y \cdot {z}^{2}\right)} \]
   3. Step-by-step derivation

      1. unpow2 72.9%

         \[\leadsto -4 \cdot \left(y \cdot \color{blue}{\left(z \cdot z\right)}\right) \]

      2. *-commutative 72.9%

         \[\leadsto -4 \cdot \color{blue}{\left(\left(z \cdot z\right) \cdot y\right)} \]

      3. associate-*l* 91.6%

         \[\leadsto -4 \cdot \color{blue}{\left(z \cdot \left(z \cdot y\right)\right)} \]

   4. Simplified 91.6%

      \[\leadsto \color{blue}{-4 \cdot \left(z \cdot \left(z \cdot y\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot z \leq 10^{-76}:\\ \;\;\;\;x \cdot x - t \cdot \left(y \cdot -4\right)\\ \mathbf{elif}\;z \cdot z \leq 2000000000000:\\ \;\;\;\;\left(z \cdot z - t\right) \cdot \left(y \cdot -4\right)\\ \mathbf{elif}\;z \cdot z \leq 5 \cdot 10^{+113}:\\ \;\;\;\;x \cdot x - t \cdot \left(y \cdot -4\right)\\ \mathbf{elif}\;z \cdot z \leq 2 \cdot 10^{+154}:\\ \;\;\;\;\left(z \cdot z - t\right) \cdot \left(y \cdot -4\right)\\ \mathbf{elif}\;z \cdot z \leq 4 \cdot 10^{+233}:\\ \;\;\;\;x \cdot x - t \cdot \left(y \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(z \cdot \left(z \cdot y\right)\right)\\ \end{array} \]

Alternative 3: 80.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot x \leq 2.7 \cdot 10^{+72} \lor \neg \left(x \cdot x \leq 6.8 \cdot 10^{+105}\right) \land x \cdot x \leq 4.2 \cdot 10^{+187}:\\ \;\;\;\;\left(z \cdot z - t\right) \cdot \left(y \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (* x x) 2.7e+72)
         (and (not (<= (* x x) 6.8e+105)) (<= (* x x) 4.2e+187)))
   (* (- (* z z) t) (* y -4.0))
   (* x x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x * x) <= 2.7e+72) || (!((x * x) <= 6.8e+105) && ((x * x) <= 4.2e+187))) {
		tmp = ((z * z) - t) * (y * -4.0);
	} else {
		tmp = x * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x * x) <= 2.7d+72) .or. (.not. ((x * x) <= 6.8d+105)) .and. ((x * x) <= 4.2d+187)) then
        tmp = ((z * z) - t) * (y * (-4.0d0))
    else
        tmp = x * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x * x) <= 2.7e+72) || (!((x * x) <= 6.8e+105) && ((x * x) <= 4.2e+187))) {
		tmp = ((z * z) - t) * (y * -4.0);
	} else {
		tmp = x * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x * x) <= 2.7e+72) or (not ((x * x) <= 6.8e+105) and ((x * x) <= 4.2e+187)):
		tmp = ((z * z) - t) * (y * -4.0)
	else:
		tmp = x * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x * x) <= 2.7e+72) || (!(Float64(x * x) <= 6.8e+105) && (Float64(x * x) <= 4.2e+187)))
		tmp = Float64(Float64(Float64(z * z) - t) * Float64(y * -4.0));
	else
		tmp = Float64(x * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x * x) <= 2.7e+72) || (~(((x * x) <= 6.8e+105)) && ((x * x) <= 4.2e+187)))
		tmp = ((z * z) - t) * (y * -4.0);
	else
		tmp = x * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x * x), $MachinePrecision], 2.7e+72], And[N[Not[LessEqual[N[(x * x), $MachinePrecision], 6.8e+105]], $MachinePrecision], LessEqual[N[(x * x), $MachinePrecision], 4.2e+187]]], N[(N[(N[(z * z), $MachinePrecision] - t), $MachinePrecision] * N[(y * -4.0), $MachinePrecision]), $MachinePrecision], N[(x * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x x) < 2.7000000000000001e72 or 6.7999999999999999e105 < (*.f64 x x) < 4.2e187

   1. Initial program 90.7%

      \[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right) \]

   2. Taylor expanded in x around 0 77.9%

      \[\leadsto \color{blue}{-4 \cdot \left(\left({z}^{2} - t\right) \cdot y\right)} \]
   3. Step-by-step derivation

      1. *-commutative 77.9%

         \[\leadsto \color{blue}{\left(\left({z}^{2} - t\right) \cdot y\right) \cdot -4} \]

      2. *-commutative 77.9%

         \[\leadsto \color{blue}{\left(y \cdot \left({z}^{2} - t\right)\right)} \cdot -4 \]

      3. unpow2 77.9%

         \[\leadsto \left(y \cdot \left(\color{blue}{z \cdot z} - t\right)\right) \cdot -4 \]

      4. *-commutative 77.9%

         \[\leadsto \color{blue}{\left(\left(z \cdot z - t\right) \cdot y\right)} \cdot -4 \]

      5. associate-*l* 77.9%

         \[\leadsto \color{blue}{\left(z \cdot z - t\right) \cdot \left(y \cdot -4\right)} \]

   4. Simplified 77.9%

      \[\leadsto \color{blue}{\left(z \cdot z - t\right) \cdot \left(y \cdot -4\right)} \]

   if 2.7000000000000001e72 < (*.f64 x x) < 6.7999999999999999e105 or 4.2e187 < (*.f64 x x)

   1. Initial program 76.1%

      \[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right) \]

   2. Taylor expanded in x around inf 83.5%

      \[\leadsto \color{blue}{{x}^{2}} \]
   3. Step-by-step derivation

      1. unpow2 83.5%

         \[\leadsto \color{blue}{x \cdot x} \]

   4. Simplified 83.5%

      \[\leadsto \color{blue}{x \cdot x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot x \leq 2.7 \cdot 10^{+72} \lor \neg \left(x \cdot x \leq 6.8 \cdot 10^{+105}\right) \land x \cdot x \leq 4.2 \cdot 10^{+187}:\\ \;\;\;\;\left(z \cdot z - t\right) \cdot \left(y \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x\\ \end{array} \]

Alternative 4: 94.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot z \leq 2 \cdot 10^{+302}:\\ \;\;\;\;x \cdot x + \left(y \cdot 4\right) \cdot \left(t - z \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(z \cdot \left(z \cdot y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z z) 2e+302)
   (+ (* x x) (* (* y 4.0) (- t (* z z))))
   (* -4.0 (* z (* z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * z) <= 2e+302) {
		tmp = (x * x) + ((y * 4.0) * (t - (z * z)));
	} else {
		tmp = -4.0 * (z * (z * y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z * z) <= 2d+302) then
        tmp = (x * x) + ((y * 4.0d0) * (t - (z * z)))
    else
        tmp = (-4.0d0) * (z * (z * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * z) <= 2e+302) {
		tmp = (x * x) + ((y * 4.0) * (t - (z * z)));
	} else {
		tmp = -4.0 * (z * (z * y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z * z) <= 2e+302:
		tmp = (x * x) + ((y * 4.0) * (t - (z * z)))
	else:
		tmp = -4.0 * (z * (z * y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * z) <= 2e+302)
		tmp = Float64(Float64(x * x) + Float64(Float64(y * 4.0) * Float64(t - Float64(z * z))));
	else
		tmp = Float64(-4.0 * Float64(z * Float64(z * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z * z) <= 2e+302)
		tmp = (x * x) + ((y * 4.0) * (t - (z * z)));
	else
		tmp = -4.0 * (z * (z * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z * z), $MachinePrecision], 2e+302], N[(N[(x * x), $MachinePrecision] + N[(N[(y * 4.0), $MachinePrecision] * N[(t - N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.0 * N[(z * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z z) < 2.0000000000000002e302

   1. Initial program 96.1%

      \[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right) \]

   if 2.0000000000000002e302 < (*.f64 z z)

   1. Initial program 58.3%

      \[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right) \]

   2. Taylor expanded in z around inf 70.5%

      \[\leadsto \color{blue}{-4 \cdot \left(y \cdot {z}^{2}\right)} \]
   3. Step-by-step derivation

      1. unpow2 70.5%

         \[\leadsto -4 \cdot \left(y \cdot \color{blue}{\left(z \cdot z\right)}\right) \]

      2. *-commutative 70.5%

         \[\leadsto -4 \cdot \color{blue}{\left(\left(z \cdot z\right) \cdot y\right)} \]

      3. associate-*l* 91.8%

         \[\leadsto -4 \cdot \color{blue}{\left(z \cdot \left(z \cdot y\right)\right)} \]

   4. Simplified 91.8%

      \[\leadsto \color{blue}{-4 \cdot \left(z \cdot \left(z \cdot y\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot z \leq 2 \cdot 10^{+302}:\\ \;\;\;\;x \cdot x + \left(y \cdot 4\right) \cdot \left(t - z \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(z \cdot \left(z \cdot y\right)\right)\\ \end{array} \]

Alternative 5: 44.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 3 \cdot 10^{-259}:\\ \;\;\;\;t \cdot \left(y \cdot 4\right)\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+56} \lor \neg \left(z \leq 4.8 \cdot 10^{+83}\right) \land z \leq 6.6 \cdot 10^{+116}:\\ \;\;\;\;x \cdot x\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(\left(z \cdot z\right) \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z 3e-259)
   (* t (* y 4.0))
   (if (or (<= z 6.6e+56) (and (not (<= z 4.8e+83)) (<= z 6.6e+116)))
     (* x x)
     (* -4.0 (* (* z z) y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 3e-259) {
		tmp = t * (y * 4.0);
	} else if ((z <= 6.6e+56) || (!(z <= 4.8e+83) && (z <= 6.6e+116))) {
		tmp = x * x;
	} else {
		tmp = -4.0 * ((z * z) * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= 3d-259) then
        tmp = t * (y * 4.0d0)
    else if ((z <= 6.6d+56) .or. (.not. (z <= 4.8d+83)) .and. (z <= 6.6d+116)) then
        tmp = x * x
    else
        tmp = (-4.0d0) * ((z * z) * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 3e-259) {
		tmp = t * (y * 4.0);
	} else if ((z <= 6.6e+56) || (!(z <= 4.8e+83) && (z <= 6.6e+116))) {
		tmp = x * x;
	} else {
		tmp = -4.0 * ((z * z) * y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= 3e-259:
		tmp = t * (y * 4.0)
	elif (z <= 6.6e+56) or (not (z <= 4.8e+83) and (z <= 6.6e+116)):
		tmp = x * x
	else:
		tmp = -4.0 * ((z * z) * y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= 3e-259)
		tmp = Float64(t * Float64(y * 4.0));
	elseif ((z <= 6.6e+56) || (!(z <= 4.8e+83) && (z <= 6.6e+116)))
		tmp = Float64(x * x);
	else
		tmp = Float64(-4.0 * Float64(Float64(z * z) * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= 3e-259)
		tmp = t * (y * 4.0);
	elseif ((z <= 6.6e+56) || (~((z <= 4.8e+83)) && (z <= 6.6e+116)))
		tmp = x * x;
	else
		tmp = -4.0 * ((z * z) * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, 3e-259], N[(t * N[(y * 4.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 6.6e+56], And[N[Not[LessEqual[z, 4.8e+83]], $MachinePrecision], LessEqual[z, 6.6e+116]]], N[(x * x), $MachinePrecision], N[(-4.0 * N[(N[(z * z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < 3.0000000000000002e-259

   1. Initial program 83.6%

      \[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right) \]

   2. Taylor expanded in t around inf 32.0%

      \[\leadsto \color{blue}{4 \cdot \left(y \cdot t\right)} \]
   3. Step-by-step derivation

      1. associate-*r* 32.0%

         \[\leadsto \color{blue}{\left(4 \cdot y\right) \cdot t} \]

   4. Simplified 32.0%

      \[\leadsto \color{blue}{\left(4 \cdot y\right) \cdot t} \]

   if 3.0000000000000002e-259 < z < 6.60000000000000004e56 or 4.79999999999999982e83 < z < 6.5999999999999996e116

   1. Initial program 97.0%

      \[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right) \]

   2. Taylor expanded in x around inf 57.2%

      \[\leadsto \color{blue}{{x}^{2}} \]
   3. Step-by-step derivation

      1. unpow2 57.2%

         \[\leadsto \color{blue}{x \cdot x} \]

   4. Simplified 57.2%

      \[\leadsto \color{blue}{x \cdot x} \]

   if 6.60000000000000004e56 < z < 4.79999999999999982e83 or 6.5999999999999996e116 < z

   1. Initial program 73.8%

      \[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right) \]

   2. Taylor expanded in z around inf 78.1%

      \[\leadsto \color{blue}{-4 \cdot \left(y \cdot {z}^{2}\right)} \]
   3. Step-by-step derivation

      1. unpow2 78.1%

         \[\leadsto -4 \cdot \left(y \cdot \color{blue}{\left(z \cdot z\right)}\right) \]

   4. Simplified 78.1%

      \[\leadsto \color{blue}{-4 \cdot \left(y \cdot \left(z \cdot z\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 47.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 3 \cdot 10^{-259}:\\ \;\;\;\;t \cdot \left(y \cdot 4\right)\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+56} \lor \neg \left(z \leq 4.8 \cdot 10^{+83}\right) \land z \leq 6.6 \cdot 10^{+116}:\\ \;\;\;\;x \cdot x\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(\left(z \cdot z\right) \cdot y\right)\\ \end{array} \]

Alternative 6: 45.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 3.8 \cdot 10^{-259}:\\ \;\;\;\;t \cdot \left(y \cdot 4\right)\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+56}:\\ \;\;\;\;x \cdot x\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+84}:\\ \;\;\;\;-4 \cdot \left(\left(z \cdot z\right) \cdot y\right)\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{+116}:\\ \;\;\;\;x \cdot x\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(z \cdot \left(z \cdot y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z 3.8e-259)
   (* t (* y 4.0))
   (if (<= z 7.8e+56)
     (* x x)
     (if (<= z 3.3e+84)
       (* -4.0 (* (* z z) y))
       (if (<= z 5.3e+116) (* x x) (* -4.0 (* z (* z y))))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 3.8e-259) {
		tmp = t * (y * 4.0);
	} else if (z <= 7.8e+56) {
		tmp = x * x;
	} else if (z <= 3.3e+84) {
		tmp = -4.0 * ((z * z) * y);
	} else if (z <= 5.3e+116) {
		tmp = x * x;
	} else {
		tmp = -4.0 * (z * (z * y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= 3.8d-259) then
        tmp = t * (y * 4.0d0)
    else if (z <= 7.8d+56) then
        tmp = x * x
    else if (z <= 3.3d+84) then
        tmp = (-4.0d0) * ((z * z) * y)
    else if (z <= 5.3d+116) then
        tmp = x * x
    else
        tmp = (-4.0d0) * (z * (z * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 3.8e-259) {
		tmp = t * (y * 4.0);
	} else if (z <= 7.8e+56) {
		tmp = x * x;
	} else if (z <= 3.3e+84) {
		tmp = -4.0 * ((z * z) * y);
	} else if (z <= 5.3e+116) {
		tmp = x * x;
	} else {
		tmp = -4.0 * (z * (z * y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= 3.8e-259:
		tmp = t * (y * 4.0)
	elif z <= 7.8e+56:
		tmp = x * x
	elif z <= 3.3e+84:
		tmp = -4.0 * ((z * z) * y)
	elif z <= 5.3e+116:
		tmp = x * x
	else:
		tmp = -4.0 * (z * (z * y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= 3.8e-259)
		tmp = Float64(t * Float64(y * 4.0));
	elseif (z <= 7.8e+56)
		tmp = Float64(x * x);
	elseif (z <= 3.3e+84)
		tmp = Float64(-4.0 * Float64(Float64(z * z) * y));
	elseif (z <= 5.3e+116)
		tmp = Float64(x * x);
	else
		tmp = Float64(-4.0 * Float64(z * Float64(z * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= 3.8e-259)
		tmp = t * (y * 4.0);
	elseif (z <= 7.8e+56)
		tmp = x * x;
	elseif (z <= 3.3e+84)
		tmp = -4.0 * ((z * z) * y);
	elseif (z <= 5.3e+116)
		tmp = x * x;
	else
		tmp = -4.0 * (z * (z * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, 3.8e-259], N[(t * N[(y * 4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.8e+56], N[(x * x), $MachinePrecision], If[LessEqual[z, 3.3e+84], N[(-4.0 * N[(N[(z * z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.3e+116], N[(x * x), $MachinePrecision], N[(-4.0 * N[(z * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < 3.8e-259

   1. Initial program 83.6%

      \[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right) \]

   2. Taylor expanded in t around inf 32.0%

      \[\leadsto \color{blue}{4 \cdot \left(y \cdot t\right)} \]
   3. Step-by-step derivation

      1. associate-*r* 32.0%

         \[\leadsto \color{blue}{\left(4 \cdot y\right) \cdot t} \]

   4. Simplified 32.0%

      \[\leadsto \color{blue}{\left(4 \cdot y\right) \cdot t} \]

   if 3.8e-259 < z < 7.79999999999999989e56 or 3.30000000000000017e84 < z < 5.3000000000000002e116

   1. Initial program 97.0%

      \[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right) \]

   2. Taylor expanded in x around inf 57.2%

      \[\leadsto \color{blue}{{x}^{2}} \]
   3. Step-by-step derivation

      1. unpow2 57.2%

         \[\leadsto \color{blue}{x \cdot x} \]

   4. Simplified 57.2%

      \[\leadsto \color{blue}{x \cdot x} \]

   if 7.79999999999999989e56 < z < 3.30000000000000017e84

   1. Initial program 100.0%

      \[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right) \]

   2. Taylor expanded in z around inf 83.6%

      \[\leadsto \color{blue}{-4 \cdot \left(y \cdot {z}^{2}\right)} \]
   3. Step-by-step derivation

      1. unpow2 83.6%

         \[\leadsto -4 \cdot \left(y \cdot \color{blue}{\left(z \cdot z\right)}\right) \]

   4. Simplified 83.6%

      \[\leadsto \color{blue}{-4 \cdot \left(y \cdot \left(z \cdot z\right)\right)} \]

   if 5.3000000000000002e116 < z

   1. Initial program 70.0%

      \[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right) \]

   2. Taylor expanded in z around inf 77.3%

      \[\leadsto \color{blue}{-4 \cdot \left(y \cdot {z}^{2}\right)} \]
   3. Step-by-step derivation

      1. unpow2 77.3%

         \[\leadsto -4 \cdot \left(y \cdot \color{blue}{\left(z \cdot z\right)}\right) \]

      2. *-commutative 77.3%

         \[\leadsto -4 \cdot \color{blue}{\left(\left(z \cdot z\right) \cdot y\right)} \]

      3. associate-*l* 92.9%

         \[\leadsto -4 \cdot \color{blue}{\left(z \cdot \left(z \cdot y\right)\right)} \]

   4. Simplified 92.9%

      \[\leadsto \color{blue}{-4 \cdot \left(z \cdot \left(z \cdot y\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 49.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 3.8 \cdot 10^{-259}:\\ \;\;\;\;t \cdot \left(y \cdot 4\right)\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+56}:\\ \;\;\;\;x \cdot x\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+84}:\\ \;\;\;\;-4 \cdot \left(\left(z \cdot z\right) \cdot y\right)\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{+116}:\\ \;\;\;\;x \cdot x\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(z \cdot \left(z \cdot y\right)\right)\\ \end{array} \]

Alternative 7: 59.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot x \leq 1.7 \cdot 10^{-23}:\\ \;\;\;\;t \cdot \left(y \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* x x) 1.7e-23) (* t (* y 4.0)) (* x x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x * x) <= 1.7e-23) {
		tmp = t * (y * 4.0);
	} else {
		tmp = x * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x * x) <= 1.7d-23) then
        tmp = t * (y * 4.0d0)
    else
        tmp = x * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x * x) <= 1.7e-23) {
		tmp = t * (y * 4.0);
	} else {
		tmp = x * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x * x) <= 1.7e-23:
		tmp = t * (y * 4.0)
	else:
		tmp = x * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x * x) <= 1.7e-23)
		tmp = Float64(t * Float64(y * 4.0));
	else
		tmp = Float64(x * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x * x) <= 1.7e-23)
		tmp = t * (y * 4.0);
	else
		tmp = x * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x * x), $MachinePrecision], 1.7e-23], N[(t * N[(y * 4.0), $MachinePrecision]), $MachinePrecision], N[(x * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x x) < 1.7e-23

   1. Initial program 91.8%

      \[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right) \]

   2. Taylor expanded in t around inf 41.8%

      \[\leadsto \color{blue}{4 \cdot \left(y \cdot t\right)} \]
   3. Step-by-step derivation

      1. associate-*r* 41.8%

         \[\leadsto \color{blue}{\left(4 \cdot y\right) \cdot t} \]

   4. Simplified 41.8%

      \[\leadsto \color{blue}{\left(4 \cdot y\right) \cdot t} \]

   if 1.7e-23 < (*.f64 x x)

   1. Initial program 78.8%

      \[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right) \]

   2. Taylor expanded in x around inf 69.8%

      \[\leadsto \color{blue}{{x}^{2}} \]
   3. Step-by-step derivation

      1. unpow2 69.8%

         \[\leadsto \color{blue}{x \cdot x} \]

   4. Simplified 69.8%

      \[\leadsto \color{blue}{x \cdot x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 56.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot x \leq 1.7 \cdot 10^{-23}:\\ \;\;\;\;t \cdot \left(y \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x\\ \end{array} \]

Alternative 8: 41.3% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ x \cdot x \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* x x))

C

double code(double x, double y, double z, double t) {
	return x * x;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x * x
end function

Java

public static double code(double x, double y, double z, double t) {
	return x * x;
}

Python

def code(x, y, z, t):
	return x * x

Julia

function code(x, y, z, t)
	return Float64(x * x)
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x * x;
end

Wolfram

code[x_, y_, z_, t_] := N[(x * x), $MachinePrecision]

Derivation

1. Initial program 85.2%

   \[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right) \]

2. Taylor expanded in x around inf 42.3%

   \[\leadsto \color{blue}{{x}^{2}} \]
3. Step-by-step derivation

   1. unpow2 42.3%

      \[\leadsto \color{blue}{x \cdot x} \]

4. Simplified 42.3%

   \[\leadsto \color{blue}{x \cdot x} \]

5. Final simplification 42.3%

   \[\leadsto x \cdot x \]

Developer target: 89.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot x - 4 \cdot \left(y \cdot \left(z \cdot z - t\right)\right) \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (- (* x x) (* 4.0 (* y (- (* z z) t)))))

C

double code(double x, double y, double z, double t) {
	return (x * x) - (4.0 * (y * ((z * z) - t)));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (x * x) - (4.0d0 * (y * ((z * z) - t)))
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x * x) - (4.0 * (y * ((z * z) - t)));
}

Python

def code(x, y, z, t):
	return (x * x) - (4.0 * (y * ((z * z) - t)))

Julia

function code(x, y, z, t)
	return Float64(Float64(x * x) - Float64(4.0 * Float64(y * Float64(Float64(z * z) - t))))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x * x) - (4.0 * (y * ((z * z) - t)));
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x * x), $MachinePrecision] - N[(4.0 * N[(y * N[(N[(z * z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2023207 
(FPCore (x y z t)
  :name "Graphics.Rasterific.Shading:$sradialGradientWithFocusShader from Rasterific-0.6.1, B"
  :precision binary64

  :herbie-target
  (- (* x x) (* 4.0 (* y (- (* z z) t))))

  (- (* x x) (* (* y 4.0) (- (* z z) t))))